The only way I've ever divided peonies is to dig them up first--allows you to see where to best cut the clump. There was a post early this spring from someone asking a similar question, think theirs was how to take a cutting from a cemetery, sentimental value to the plant. There was a reply from someone about taking a piece from one side, you might want to try to find that post and read it. I don't remember the username of the poster or who replied, sorry.
As far as asking for a division, I've never asked anyone I didn't know for a piece of rootball. I've certainly asked to collect seed or get a small cutting of new growth. You might want to suggest some type of trade--maybe you have something in your garden that might look good with their peony?

Planting depth depends on your hardiness zone. It doesn't have to be planted at the exact same depth as it was before but the colder the zone, the deeper the rootball should be. You'd have to be in a pretty cold zone to go deeper than an inch or so, though--I'm zone 5, bordering on zone 4B, and I plant mine so that the eyes on the rootball are barely covered, 1/2 inch or so at most below dirt. I do mulch pretty heavily to conserve moisture so that certainly adds to the depth. If you mulch, you absolutely need to move the mulch away from the emerging growth in early spring.

Good luck acquiring the peony you have your eye on!

When the peony dies down in the fall, they might feel more inclined to allow you to take off a slice from the growing edge. I have done so many times without digging up the whole plant, with no damage to the mother plant, or affecting next years bloom. For now spend some time getting to know them, and be sure they do own the property and are not just renting or leasing it. Al